$\dfrac{ 9c + 9d }{ 7 } = \dfrac{ -9c - 3e }{ 6 }$ Solve for $c$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ 9c + 9d }{ {7} } = \dfrac{ -9c - 3e }{ 6 }$ ${7} \cdot \dfrac{ 9c + 9d }{ {7} } = {7} \cdot \dfrac{ -9c - 3e }{ 6 }$ $9c + 9d = {7} \cdot \dfrac { -9c - 3e }{ 6 }$ Multiply both sides by the right denominator. $9c + 9d = 7 \cdot \dfrac{ -9c - 3e }{ {6} }$ ${6} \cdot \left( 9c + 9d \right) = {6} \cdot 7 \cdot \dfrac{ -9c - 3e }{ {6} }$ ${6} \cdot \left( 9c + 9d \right) = 7 \cdot \left( -9c - 3e \right)$ Distribute both sides ${6} \cdot \left( 9c + 9d \right) = {7} \cdot \left( -9c - 3e \right)$ ${54}c + {54}d = -{63}c - {21}e$ Combine $c$ terms on the left. ${54c} + 54d = -{63c} - 21e$ ${117c} + 54d = -21e$ Move the $d$ term to the right. $117c + {54d} = -21e$ $117c = -21e - {54d}$ Isolate $c$ by dividing both sides by its coefficient. ${117}c = -21e - 54d$ $c = \dfrac{ -21e - 54d }{ {117} }$ All of these terms are divisible by $3$ $c = \dfrac{ -{7}e - {18}d }{ {39} }$